Measurement of flow rate, velocity profile and friction factor in Pipe

Flow

S. Ghosh, M. Muste, M. Marquardt, F. Stern

Overview

Purpose Experimental design Experimental Process Test Set-up Data acquisition Data reduction Uncertainty analysis Data analysis

Purpose Provide hands-on experience with pipe stand facility and modern measurement systems including pressure transducers, pitot probes and computer data acquisition and data reduction.

Comparison between automated and manual data acquisition systems.

Measure flow rate, velocity profiles and friction factor in smooth and rough pipes.

Determine experimental uncertainties.

Compare results with benchmark data

Experimental DesignThe facility consists of:Closed pipe networkFanReservoir

Instrumentation:3 Venturi meters

Simple water ManometerDifferential Water manometerPitot ProbeDigital Micrometer (Accurate radial positioning)

Pressure transducer

Computer based Automated Data Acquisition System (DA)

Contraction Diameters (mm):

12.7 25.4 52.93

Flow Coefficient, K 0.915 0.937

0.935

Experimental process Data

Analysis

Compare results with benchmark data, CFD, and

/or AFD

Use Fig 8 as reference value

for velocity profile

Plot experimental velocity profile

and friction factor on

reference data

Use Fig 9 as reference value

for friction factor

Evaluate fluid physics, EFD

process and UA

Answer questions in

section 4

Report difference between

experimental and reference data

Prepare report

Data Reduction

Statistical analysis

Data reduction equations

Remove outliers

Evaluate Eq. 3

Evaluate Eq. 4

Uncertainty Analysis

Estimate bias limits

Table 1

Estimate precision limits

Evaluate Eq. 9

Evaluate Eq. 13

Estimate total uncertainty

Evaluate Eq. 7

Evaluate Eq. 11

Test Set-up

Facility & conditions

Prepare measurement

systems

Venturimeter

Pressure transducer

Valve manifold

Pitot tube

Micrometer

Install model

N/A

Calibration

N/A

Data Acquisition

Prepare experimental procedures

Run tests & acquire data

Store data

Write results to output file

Measure room and pipe

temperature

Initialize data acquisition software

Open Labview program

Set blower speed

Set valves in proper

positions

Airflow pipe system

Enter hardware settings

Measure total discharge

Measure velocity profile

Measure pressure drop in pipe

Repeat discharge measurement

Evaluate Eq. 5

Evaluate Eq. 6

Test set-up

Test Set-up: Venturi meter and Pitot-tube housing

Venturimeter Pitot-tube housing

Test set-up: Instrumentation

The equipment used in the experiment includes:

Digital thermometer with a range of – 40 to 450 F and a smallest reading of 0.1 F for measurement of the environment temperature.

Digital micrometer with least significant digit 0.01 mm for positioning the Pitot-tube inside the pipe.

Simple water manometer with a range of 2.5 ft and a least scale division of 0.001 ft for measurement of the head at each pressure tap along the pipes and for measurement of velocities using the Pitot-tube arrangement .

Differential water manometer with a range 3 ft and a least scale division of 0.001ft for measurement of the head drop across the Venturi meters. Pressure transducer calibrated with ft of water

Test set-up: Instrumentation

Reservoir:To build up pressure and force the air

to flow downstream through any of the three straight experiment pipes.

Digital Micrometer:Allows the measurement of the

position of the Pitot probe at different locations along the cross section of the pipe tested

Pitot Probe:Located in the glass-wall boxUsed to measure the Stagnation

pressure and calculate the velocity profile in pipe

Venturi meters:Located on each pipe typeUsed to measure flow rate Q along the

differential water manometer

Pressure Taps:Located along each pipe, they are

connected to the simple water manometer to evaluate the head measurement

They are used to calculate the friction factor

Manometers:To measure the head at each pressure

Tap along the pipe and to make the Pitot-tube measurements (simple Manometer)

To measure head drops across the venturi meters (differential Manometer)

Data acquisitionThe procedures for data acquisition and reduction are described as follow:

1. Use the appropriate Venturi meter, (2” contraction diameter) to measure the total discharge. Increase blower setting from 15% to 35% with 5% increments and measure flow rate using both manometer and pressure transducer.

2. Take reading for ambient air (manometer water) and pipe air temperatures.

3. To obtain velocity data, use the Pitot-tube box to measure the ambient head and stagnation heads across the pipe. Measure the stagnation heads at radial intervals. The recommended radial spacing for one half of the diameter is 0, 5, 10, 15, 20, 23, and 24 mm.

4. Maintaining the discharge at 35%, measure the head along the pipe by

means of the ADAS the pressure heads at pressure taps 1, 2, 3, and 4

5. Repeat step 2

Automated Data Acquisition System

Layout of the data acquisition systems: a) photo; b)

schematic

(a) (b)

D A 2 D A 1

Tes te d P ipe

P ito t-Tu beH o us in g

S ta ticP ressu re

S ta gn a tio nP ressu re

S ta tic P re ssure from P ressu re Ta ps

Ve ntur i M eter

P ressu reTran sd uce r

Va lveM a nifo ld

R e tu rn P ip e

S im pleM a no m ete r

D iffe ren tia lM a no m ete r

Tyg on Tu b in gC o nn ec tion s

LEGEND

ToAtmosphereTo

Atmosphere

Introduction to ADAS Software - Labview

Front panel on Data Acquisition program

Initial settings

Flow rate measurement

Friction factor measurement

Velocity profile measurement

Data reduction

For the flow rate and friction factor, the individual measurements are performed for:

Ambient air temperature Pipe air temperature Pipe pressure head Venturi meter pressure head

drop

The experimental Results are:

Manometer water density Air density Kinematic viscosity Flow rate Reynolds number Friction factor

Data reduction equations are: )( o

ww Tf)( o

airair Tf )( oairair Tf

air

wDMt ZgKAQ

2

aire D

QR

4

ji SMSM

air

w ZZLQ

Dgf

2

52

8

Data reduction equations: Flow rate

)(22

22

Bernoullig

V

g

p

g

V

g

p bbaa

)(ContinuityAVAV bbaa

Volumetric flow rate bbVAQ

,

,)1(2

22

22

ba

baD

a

w

ba

baD

AA

AACK

ghAA

AACQ

a

wDMt zgKAQ

2Equation (1), lab handout

Friction factor

D A 2 D A 1

Tes te d P ipe

P ito t-Tu beH o us in g

S ta ticP ressu re

S ta gn a tio nP ressu re

S ta tic P re ssure from P ressu re Ta ps

Ve ntur i M eter

P ressu reTran sd uce r

Va lveM a nifo ld

R e tu rn P ip e

S im pleM a no m ete r

D iffe ren tia lM a no m ete r

Tyg on Tu b in gC o nn ec tion s

LEGEND

ToAtmosphereTo

Atmosphere

Friction factor (contd.)

jSMiSMa

w zzLQ

Dgf

2

52

8

Equation 2 is a form of Darcy Weisbach equationin terms of flow rate Q and pressure drop where, and A is the pipe cross sectional area.

Velocity profile

/)(2

,2

1

0

20

stat

stat

ppV

BernoulliVpp

2/1

2)(

StaticStagnation SMSMa

w zrzg

ru

Equation 3, Exercise notes

stag

SMSMwstatstag

pp

zzgppstatstag

0

);(

Data reduction: Spreadsheet

Spreadsheet for data acquisition, data reduction and uncertainty analysis for Measurement of Velocity profile and friction factor in pipe flows (smooth pipe)

Table of ContentsColor code:

1. Experimental Summary Sections2. Data reduction equations Comments3. Data Acquisition and Reduction Enter student data 3.1 Input variables Constants 3.2 Measured variables Calculated or output values4. Uncertainty Analysis 4.1 Bias Limits 4.2 Precision Limits 4.3 Total Uncertainty

1. Experiment summaryStatement of Purpose: To measure velocity profile and friction factor

in rough pipe and determine the uncertainties and compare results with benchmark data.

Facility: Air-flow unit (WTA)Test Design: Air flows through a pipe systemReferences: Lab2 Handout: http://css.engineering.uiowa-

.edu/~fluids/Lab/EFDLab2.PDF

2. Data Reduction Equations

3. Data acquisition and reduction for multiple test UA approach3.1 Input variables

Quantity Symbol Value UnitsGravity g 9.8031 m/s^2Number of test M 10 -----Coverage factor for standard deviation K 2 -----

3.2 Measured variablesThe following example illustrates the procedure for calculating Q using velocity

Date Time For calculating the flow rate Q (Cell no. G66) first obtain the velocity profile with respect to radial distance. Cells D84-D98 calculates the velocity profile.

Re= Room Pipe The following example illustrates the procedure for calculating Q using velocityInitial integration method. Note: The x axis on the following plot is cell A85 - A91. The

ZDM= Final Y axis is cell D85 - D91. Once the velocity profile is plotted, fit a 2nd order polynomial

Average ###### #DIV/0! curve to the points and display the equation on the chart, as shown below. The y in theequation is velocity and the x is radial distance r. Finally the flow rate Q is given by the following formula. Note that the variable x in the integral equation is actually radius.

Initial Also Rmax is the radius of the pipe.

FinalAverage Avera

ge

TAP # Locationz SM

(ft water)

(ft) z SM4

(ft water)f 34

1 5 #DIV/0!2 f 12 = #DIV/0! 10 #DIV/0!3 f 23 = #DIV/0! 15 #DIV/0!4 f 34 = #DIV/0! 20 #DIV/0!

#DIV/0!Symbol Value Units #DIV/0!

K 0.935 #DIV/0!At 0.002154 m2 #DIV/0!

g 9.8031 m/s2 #DIV/0!D 0.05238 m #DIV/0!L 9.144 m #DIV/0!

#DIV/0!

r (m)

z SM stagnatio

n (ft z SM static

(ft

u (m/s)

Measur. #

0.026 0.000 10.024 #DIV/0! 20.023 #DIV/0! 30.020 #DIV/0! 40.015 #DIV/0! 50.010 #DIV/0! 60.005 #DIV/0! 70.000 #DIV/0! 8 Note: The value in cell G 66 for the flow rate should be approximately-0.005 #DIV/0! 9 0.07 m3/s. Check your flow rate calculation of your value deviates-0.010 #DIV/0! 10 too much from the recommended value.-0.015 #DIV/0! Average -0.020 #DIV/0! Std. Dev Conversion of pressure head from ft of water to pascals-0.023 #DIV/0!-0.024 #DIV/0! Tap # ZSM(ft water) ZSM pas-0.026 0.0000 1 0.0000 0

2 0.0000 03 0.0000 04 0.0000 0

Alternate measurements at various radial positions with repeated measurements.

#DIV/0! #DIV/0! #DIV/0!#DIV/0! #DIV/0! #DIV/0!

#DIV/0!#DIV/0!

#DIV/0!#DIV/0!

#DIV/0!#DIV/0!

#DIV/0!#DIV/0!

#DIV/0!#DIV/0!

VELOCITY PROFILE Repeated Measurements (near wall)z SM stagnation

(ft water)z SM static

(Ft water)u

(m/s)

Pipe Diameter 10Pipe Length Average f 34

St. Deviation Sf34

Cross-sectionArea 8

Gravity 9

Constant 6Discharge Coeff. 7

4

5

23

f i j Measur.. #

z SM3

(ft water)

1

FRICTION FACTOR Repeated MeasurementsSmooth Pipe Smooth Pipe

Average #DIV/0! #IV/0!

Venturi Head Drop z DM (ft water) Flow Rate Q (m3/s) Reynolds Number (Re)Initial from integration of velocity

profileFinal

0.59 a (kg/m3) =

m a (kg/m.s) =

Actual Flow rate

Temperature(deg C) Fluid Property100,000

Target Headdrop (ft water) w (kg/m3) =

Appendix C:

Target ConditionsTarget Reynolds #

2/1

2)(

StaticStagnation SMSMa

w zrzg

ru jSMiSM

a

w zzLQ

Dgf

2

52

8 Eqn. (3) Eqn. (4)

Table A1.

Table A2.

xdxxxQRmas

)434.4111.2872733(20

2

Uncertainty analysis

Block diagram of the experimental determination of the Friction factor

Block diagram of the Velocity measurement

EXPERIMENTALRESULTS

EXPERIMENTAL ERROR SOURCES

INDIVIDUALMEASUREMENT

SYSTEMS

MEASUREMENTOF INDIVIDUAL

VARIABLES

DATA REDUCTIONEQUATIONS

TEMPERATUREWATER

TEMPERATUREAIR

fB , P

VENTURIPRESSURE

PIPEPRESSURE

f = F( , , z , Q = )a

a

wg D

8LQ

Q = F( z )

w

w

T

TB T, P

z

zB , P

f f

SM

SMww

DM

SM

2

2

5

aT

TB T, Paa

z SM

z

zB , PDM

DM z DM

= F(T )

( )

w

= F(T )a

zSM i

- zSM j

w

a

EXPERIMENTALRESULT

w

w

T

TB T, P

STAGNATIONPRESSURE

STATICPRESSURE

EXPERIMENTAL ERROR SOURCES

INDIVIDUALMEASUREMENT

SYSTEMS

MEASUREMENTOF INDIVIDUAL

VARIABLES

DATA REDUCTIONEQUATIONS

z

B , PSM

B , Pu u

u

= F(T )

u = F( , , z , z ) 2( ) g

½

=

TEMPERATUREWATER

TEMPERATUREAIR

w

a stag

a

T

TB T, Pa

z

w

w

w

SMstag

zSM

stag

z

B , PSM stat

zSM

stat

zSM

stat

= F(T )a

aa SM

stagSM

stat

zSM stag

- zSM stat

w

a

Uncertainty Analysis

The data reduction equation for the friction factor is:

However here we will only consider bias limits for ZSM i and ZSM j . The total uncertainty for the friction is:

The Bias Limit, Bf and the precision limit, Pf, for the result are given by:

222fff PBU

2222

1

222

jSMSMjiSMiSM ZZZZ

j

iiif BBBB

M

tSP f

f

jSMiSMa

w zzLQ

Dgf

2

52

8

Uncertainty Analysis (continue)

Data Reduction equation for the velocity profile is as follow:

222uuu PBU

2222

1

222

statSMstatSMSMstagnstagnSM ZZZZ

j

iiiu BBBB

M

tSP uu

2/1

2)(

StatStag SMSMa

w zrzg

ru

Data Analysis: Results and discussions

10 104

10 10 10 105 6 7 83

0 .008

0 .009

0 .015

0 .025

0 .020

0 .010

0 .030

0 .040

0 .050

0 .060

0 .070

0 .080

0 .090

0 .10

R eynolds N umber, R e = VD

Fric

tion

Fac

tor

f =h

f

(L/D

)V /

(2g)

2

0 .00001

0 .00005

0 .0001

0 .0002

0 .00040 .00060 .00080 .001

0 .050 .04

0 .03

0 .02

0 .01

0 .015

0 .0080 .006

0 .004

0 .002

Rel

ativ

e R

ough

ness

, /D

Lam ina rF low

Critica lZ one

T rans itionZ one

/D = 0 .000005

/D = 0 .000001

Com p le te T u rbu lence , Hyd rau lica lly Rough

Hyd rau lica lly S m oo th

k

k

k

Smooth Pipe (2”) low speed

Rough Pipe (2”) low speed

07/10/03

Benchmark data for Friction Factor

Moody Chart for pipe friction with smooth and rough walls

Low speed = 44 m/s

Data Analysis: Results and discussions (contd.)

r/R u/umax

0.0000 1.0000

0.1000 0.9950

0.2000 0.9850

0.3000 0.9750

0.4000 0.9600

0.5000 0.9350

0.6000 0.9000

0.7000 0.8650

0.8000 0.8150

0.9000 0.7400

0.9625 0.6500

0.9820 0.5850

1.0000 0.4300

Benchmark data for velocity profile (Schlichting, 1968)

0

0. 2

0. 4

0. 6

0. 8

1

-1 -0. 8 -0. 6 -0. 4 -0. 2 0 0. 2 0. 4 0. 6 0. 8 1

r / R

Rough pipe - Low Speed

Smooth pipe -Low Speed

Rough P ipe - High Speed

Smooth P ipe - High speed

Schlichting Data

Low speed = 44 m/sHigh speed = 62 m/s

PIV-Particle Image Velocimetry

• PIV Process 1. Inject flow with Particles2. Illuminate particles with Light3. Take snapshots of the particles with a

Camera4. Process Images with Software

•PIV Equipment• Particles : Very small, neutrally

buoyant, and “reflective”.• Light: Generated using lasers, LEDS,

… and formed into a thin sheet of light

• Camera: Digital camera capable of taking images at a fast rate

• Images: Show movement of particles with stark contrast

• Software: Analyzes patterns of particles, now pixels, and tracks there displacement

PIV-continued• PIV Fundamentals-abridged

-PIV measures whole velocity fields by taking two images shortly after each other and calculating the distance individual particles travelled within this time. From the known time difference and the measured displacement, the velocity can be calculated

• Benefits of PIV -Pitot tube, thermal anemometers, laser Doppler velocimetry,…only measure velocity at points of the flow→PIV measures entire cross section or volume of flow

PIV-Continued

• PIV Fundamentals-fine details

•Two camera images are divided in to similar small tiles, called interrogation windows. •A pattern of particles is detected in the interrogation window•The predominant movement of the pattern from the first image to the second is measured •The displacement of the pattern from the first to the second image is measured in pixel dimensions•The spatial dimensions of the image are correlated to the pixel dimensions•The spatial displacement divided by the time interval of images →velocity

PIV-Continued

• PIV uses for Lab 2•Apply the continuity equation to flow field measurements•Calculate flow rate across a varying cross section orifice

• PIV steps for Lab 2•Take at least two images of the flow•Analyze the images•Extract the raw velocity field measurements•Sample velocity data from two transverse cross sections of the flow•Extract the mean stream wise velocity components from each cross section •Multiply the mean velocity by cross sectional area to find flow rate

PIV-Continued

• PIV equations

Stream wise velocity component

Average flow rate

The End